Hello Habibi,

I am assuming that you are asking if there are some materials which exhibit both pile-up AND sink-in around indentations at the same time. This would be considered quite unusual behavior but surprisingly it can happen during indentation of highly anisotropic / low symmetry SINGLE crystals (particularly ones with high Young's modulus to hardness ratios).

In some single crystals, easy plastic flow of material can be limited to only a few slip or twin system. In these cases, if an indenter edge is favorably oriented to activate an easy slip/twin system, then large pile-up can occur along this edge. If another indenter edge is unfavorably oriented for activating an easy slip/twin system, then sink-in can occur around this edge.

This is still uncommon behavior, even in single crystals, but should be more of a concern when there is very, very low symmetry along the crystallographic direction of the indenter loading axis. If you want to find papers on this, I'd look for articles on the indentation of minerals with in-situ SEM (if those exist...).

More generally, this type of behavior could only be exhibited in a material with significant elastic anisotropy and/or very limited slip/twin systems.

Best,

--Zach